Abstract
In this paper, mathematical modeling is treated as distinct from curve fitting. Considerations of psychological reality behind our data are emphasized, and criteria such as additivity in a model its natural generalization to a continuous response model, satisfaction of the unique maximum condition and orderliness of the modal points of the operating characteristics of the ordered polychotomous responses are proposed. Strengths and weaknesses of mathematical models for ordered polychotomous responses that include the normal ogive model, the logistic model, the acceleration model and the family of ordered polychotomous models developed from Bock’s nominal model are observed and discussed in terms of such criteria. It was concluded that it will be better to leave Bock’s model as a nominal model as he intended it to be, without expanding it to ordered polychotomous models.
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Samejima, F. Evaluation of Mathematical Models for Ordered Polychotomous Responses. Behaviormetrika 23, 17–35 (1996). https://doi.org/10.2333/bhmk.23.17
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DOI: https://doi.org/10.2333/bhmk.23.17